\[ y''(x)=-\frac {y(x) (a b x-\alpha \beta )}{(x-1) x^2}-\frac {y'(x) (x (a+b+1)+\alpha +\beta -1)}{(x-1) x} \] ✓ Mathematica : cpu = 0.266339 (sec), leaf count = 52
\[\left \{\left \{y(x)\to (-1)^{\alpha } c_1 x^{\alpha } \, _2F_1(a+\alpha ,\alpha +b;\alpha -\beta +1;x)+(-1)^{\beta } c_2 x^{\beta } \, _2F_1(a+\beta ,b+\beta ;-\alpha +\beta +1;x)\right \}\right \}\]
✓ Maple : cpu = 0.139 (sec), leaf count = 103
\[ \left \{ y \left ( x \right ) ={\it \_C1}\, \left ( x-1 \right ) ^{1-a-\alpha -b-\beta }{x}^{\alpha }{\mbox {$_2$F$_1$}(1-a-\beta ,1-b-\beta ;\,1-\beta +\alpha ;\,x)}+{\it \_C2}\, \left ( x-1 \right ) ^{1-a-\alpha -b-\beta }{x}^{\beta }{\mbox {$_2$F$_1$}(1-\alpha -b,1-a-\alpha ;\,1+\beta -\alpha ;\,x)} \right \} \]